Two production lines have different defect rates. Which test would compare their defect proportions?

Two production lines have different defect rates. Which test would compare their defect proportions?

• A. 2-proportion z-test
• B. 1-proportion z-test
• C. Paired t-test
• D. Chi-square test

Answer: (A)

Comparing defect proportions from two independent production lines is a two-proportion z-test. You’re testing whether the true defect rates differ between the two lines, using the observed proportions of defects from each line (p1_hat and p2_hat). Because the defect outcome is binary, each line provides binomial data, and with enough observations the difference between the two proportions is approximately normal under the null hypothesis that p1 = p2. The test statistic measures how far the observed difference is from zero relative to the standard error estimated under that null, often using a pooled proportion if the null assumes equal rates. If the difference is large enough, you reject that the lines share the same defect rate. This is the most direct method for two independent proportions. A one-proportion z-test would compare a single line to a fixed rate, not to the other line; a paired t-test is for means on matched pairs; a chi-square test can also handle this data in a contingency-table framework, but the two-proportion z-test is the standard direct approach for comparing two proportions.

Comparing defect proportions from two independent production lines is a two-proportion z-test. You’re testing whether the true defect rates differ between the two lines, using the observed proportions of defects from each line (p1_hat and p2_hat). Because the defect outcome is binary, each line provides binomial data, and with enough observations the difference between the two proportions is approximately normal under the null hypothesis that p1 = p2. The test statistic measures how far the observed difference is from zero relative to the standard error estimated under that null, often using a pooled proportion if the null assumes equal rates. If the difference is large enough, you reject that the lines share the same defect rate. This is the most direct method for two independent proportions. A one-proportion z-test would compare a single line to a fixed rate, not to the other line; a paired t-test is for means on matched pairs; a chi-square test can also handle this data in a contingency-table framework, but the two-proportion z-test is the standard direct approach for comparing two proportions.